Rigorous Inequalities Between Length and Time Scales in Glassy Systems

Authors: Montanari, Andrea; Semerjian, Guilhem

Source: Journal of Statistical Physics, Volume 125, Number 1, October 2006 , pp. 23-54(32)

Publisher: Springer

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Abstract:

Glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order. It is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length. We prove rigorous bounds between length and time scales implying the growth of a properly defined length when the relaxation time increases. Our results are valid in a rather general setting, which covers finite-dimensional and mean field systems.

As an illustration, we discuss the Glauber (heat bath) dynamics of p-spin glass models on random regular graphs. We present the first proof that a model of this type undergoes a purely dynamical phase transition not accompanied by any thermodynamic singularity.

Keywords: glass transition; Glauber dynamics; correlation time; correlation length

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10955-006-9175-y

Affiliations: 1: Email: montanar@lpt.ens.fr

Publication date: 2006-10-01